Geoscience Reference
In-Depth Information
6 Gravity field outside
the earth
6.1
Introduction
The gravity field outside the earth is particularly important at satellite al-
titude; this will be treated mainly in Chap. 7. The considerations of the
present chapter are applicable to gravitational forces also at satellites (see
Sect. 7.2), but their main practical purpose is to compute test values for the
gravity vector, gravity disturbances, and gravity anomalies at flight eleva-
tions for comparison with airborne gravimetry for reference and calibration
purposes. Airborne gravimetry is much faster than both terrestrial and ship-
borne gravimetry, so it is of interest also for geophysical prospecting.
For computational reasons, it is again convenient to split the gravity
potential
W
and the gravity vector
g
=grad
W
(6-1)
into a normal potential
U
and a normal gravity vector
γ
=grad
U,
(6-2)
and the disturbing potential
T
=
W
−
U
and the gravity disturbance vector
δ
g
=grad
T
=
g
−
γ
.
(6-3)
The normal gravity field is usually taken to be the gravity field of a suit-
able equipotential ellipsoid. This permits closed formulas and offers other
advantages of mathematical simplicity (see Sect. 2.12).
Thus,
U
and
γ
are computed first, and
W
and
g
are then obtained by
W
=
U
+
T,
(6-4)
g
=
γ
+
δ
g
.
For some purposes, we need the vector of gravitation, grad
V
(pure at-
traction without centrifugal force), rather than the vector of gravity. The
gravitational vector is computed from the gravity vector by subtracting the
vector of centrifugal force:
⎡
⎤
ω
2
x
ω
2
y
0
⎣
⎦
,
grad
V
=
g
−
grad Φ =
g
−
(6-5)
